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Six weeks before his election as London mayor in 2008, Boris Johnson unveiled his housing manifesto. “If we are to improve the quality of life for all Londoners,” he told an audience at the Royal Institute of British Architects, “then we must do something about the impact housing has on the rising cost of living.”

The challenge of making homes more affordable was to prove beyond the mayor during his two terms and eight years in the post. At the time of his election, first-time buyers were spending on average 6.5 times their annual earnings on a home, according to Nationwide building society; now, the figure is 10.4 times (up from 2.8 times in the early 1990s). Rents, meanwhile, have risen 48 per cent since 2007 against 11 per cent for incomes, according to Countrywide, the estate agency group.

Long a worry for workers, the affordability of London housing has become a prime concern for companies: in a survey by the CBI, the employers’ organisation, ahead of this year’s mayoral election, it came second only to transport as a priority for businesses. The London media have featured stories of “extreme renting” by young residents who attempt to avoid high housing costs by living in minuscule apartments, boats and even garages.

Few blame Johnson alone for the housing affordability crisis. With limited powers as mayor, he had to contend with intense demographic pressures. In 2015, the capital exceeded its 1939 population record of 8.61m, reaching a new high of 8.63m, according to the Greater London Authority. But during his tenure he faced fierce opposition to a succession of projects waved through with low proportions of affordable housing, including a large regeneration scheme at Earl’s Court, the site of the former exhibition centre in west London.

A big redevelopment at Elephant and Castle in south London also faced angry opposition because only 25 per cent of it was affordable housing — below the borough of Southwark’s supposed minimum of 35 per cent — and it will lead to a loss of homes at significantly reduced rents, known as social rents. More broadly, Johnson established a pattern of pushing through developments that had been rejected by local authorities.

Early in his mayoralty, the Conservative politician came under fire for dropping a target put in place by his Labour predecessor, Ken Livingstone, that 50 per cent of all new homes should be affordable. But he actually beat Livingstone’s annual average of affordable housing construction by about 1,600 homes, according to GLA figures. He did, however, have the benefit of a wider definition of affordable housing from 2011, which included rents of up to 80 per cent of the market rate.

A new block of affordable homes near Elephant and Castle, beside older local authority housing

The arrival of the new mayor, Labour’s Sadiq Khan, in May this year followed an election in which voters identified housing as their top priority. This offered a chance to take stock. Since taking office, Khan has begun an overhaul of the processes by which most affordable housing is now built. Developers currently negotiate with councils on levels of cheaper housing through an adversarial and unpopular process of “viability assessments” on each project. Instead, says Khan’s deputy mayor for housing, James Murray, the administration will probably allow projects with a specified threshhold of affordable homes — potentially 35 per cent — to skip the viability process.

In planning guidance to be released this autumn, Khan’s team is also likely to introduce a new definition of “affordable” rents. Murray favours a tougher definition based on median earnings. These measures will affect the quantity and nature of affordable housing provided under so-called Section 106 agreements, which require commercial developments to include below-market housing. But they will not change the capital’s overall reliance on these agreements, which in effect piggyback on profit-making schemes that often stall when property markets drop.

James Murray, the deputy mayor of London for housing and residential development

That problem has come to the fore since the UK voted to leave the EU, which has injected uncertainty into the housing market. “Almost all affordable housing depends on private sector development, and [the Brexit vote] will likely slow the pace of that development,” says Ben Rogers, director at the Centre for London think-tank. “There are also worries about the thing that really unlocks new housing in London, which is new infrastructure. A project like Crossrail 2 [a proposed north-south rail link] depends on a great deal of parliamentary legislation, and is there going to be time for that legislation if we are uncoupling ourselves from Europe?”

Even without that factor, industry leaders agree that more drastic changes are needed to bring about a big increase in construction. Khan puts the overall number of new homes that the capital needs to build each year at 50,000, but in 2015 the figure was only 24,610 — and that was the highest total in a decade.

Despite the acute need for new housing, construction in recent years has fallen far short of 20th-century peaks: London built 37,400 new homes in 1971, when the number of households in the capital was a third lower than today, and 80,600 in 1934, when the city’s population was approaching current levels.

During these peaks, construction was less reliant on private-sector housebuilders, since local authorities were prolific builders in their own right. Additionally, land was cheaper and planning regimes were less restrictive of development. The most recent housebuilding boom “was a great national effort”, says Stuart Robinson, chairman of planning at CBRE, the property advisers. “This time there are so many bodies competing for labour and capital and materials. We lived in a world then when people didn’t object to housing; they just allowed councils to get on with it. Now, the fundamental nature of British society has changed. We don’t seem to encourage those organisations that are seeking to provide housing through other means than housing for sale.”

Almost all affordable housing depends on private sector development. The Brexit vote will likely slow the pace of that

Ben Rogers, Centre for London

At City Hall, Murray is aware of the need to bring fresh sources of capital into housebuilding. He is looking at ways to use the planning system to encourage more construction of “build-to-rent” developments — large schemes that are popular among big financial institutions seeking steady income.

But the key to achieving significant change, says Rogers, is devolution, specifically control over more public funds. Johnson took control of housing policy and spending in the capital; Rogers believes his successor should seek both devolution of the stamp duty regime on properties and council tax reform, enabling additional receipts to councils that could fund housing development.

Khan is in discussions with central government on further devolution, and has received an early positive response from the Treasury. He is also “making the case that councils should have more flexibility to invest”, says Murray.

We need to step up the unlocking of public land for housing

Stephen Howlett, Peabody

Stephen Howlett, chief executive of Peabody, the housing association, believes Khan should also step up his predecessor’s efforts to unlock public land. “There’s been lots of talk about public land being made available for housing, and some progress has been made, but we need to step it up a gear. That’s an issue for the mayor and for central government as well,” he says.

In the meantime, debate rages over the changes Khan plans to make to the existing regime. One hope is that tougher demands on affordable housing might help to bring down prices for development land, opening up new opportunities. But CBRE’s Robinson worries these same demands might “create a lot of undevelopable land” by making construction yet more expensive.

At the same time, Robinson has faith in the mayor’s potential as a catalyst for broader changes. “You don’t have a lot of power, but you do have a lot of influence,” he says. “He can use his influence to align people’s actions.”

Protesters derail high-rise scheme

Bishopsgate Goodsyard in its current state

Between the City of London and the booming Shoreditch technology belt to the north-east lie 11 acres of disused railway arches, wild plants and temporary football pitches — this despite the plot’s prime location next to an Overground station.

Bishopsgate Goodsyard is one of several promising London sites that still stands empty thanks to wrangling over the nature and purpose of its redevelopment.

The site was bought by the listed property company Hammerson and developers Ballymore in the early 2000s after laying derelict since a fire destroyed its contents, and killed two people, in 1964.

The original concept for the £800m redevelopment

The property companies proposed an £800m plan to redevelop the site, including seven towers between 17 and 46 storeys high, but have faced stiff opposition from a campaign led by Dan Cruickshank, the art historian and BBC television presenter. The campaign has highlighted the lack of other skyscrapers in the immediate area, the shadows the towers would cast and a low level of affordable homes — 15.8 per cent under the latest plans. The developers counter that their plans offer more than 1,350 new homes, 700,000 sq ft of office space and 5.5 acres of new “public realm”, including a raised park.

Boris Johnson left the final decision on the Goodsyard to his successor as mayor, Sadiq Khan, after his planning officers recommended rejecting the scheme. Khan issued a signal to developers by hiring the former mayor of Hackney and a prominent opponent of the scheme, Jules Pipe, as his new planning chief.

Once again, the scheme has gone back to the drawing board: Hammerson says it will take another 12 months to reconsider its plans.

Prime market feels the pain

Eaton Square in the prime district of Belgravia

After the 2008 financial crisis, London’s high-end residential sector recovered quickly, as overseas investors showed a seemingly limitless appetite for homes in exclusive areas such as Kensington and Chelsea.

But the Brexit shock comes as the sector is already in decline again, hit by repeated changes to the stamp duty regime, a fresh wave of new supply being built and a waning of demand from Asian and Russian buyers.

The number of properties that changed hands in the second quarter of 2016 in prime London areas was down 42 per cent on the same period a year earlier, according to LonRes, a research company, which also noted a wave of discounting in the aftermath of the referendum, as some vendors finally conceded that prices were falling.

“Over the past 18 months vendors had already begun to adapt to the new pricing environment, and in many cases Brexit has been a trigger to make overdue reductions to asking prices,” says Liam Bailey, head of residential research at property advisers Knight Frank.

Prices in London’s wealthiest areas were down 3.9 per cent from a year earlier in the second quarter of 2016, and 8 per cent below their 2014 peak, according to Savills, the estate agency.

Oliver Hooper, director at Huntly Hooper, the property search firm, says he has seen one vendor offer to take a 30 per cent loss on the price they paid for a home. But more generally, he adds, “the ownership of the prime central London market is fairly affluent, and on the whole, vendors are holding out”.

Estate agents have found one ray of hope since the referendum: the decline in sterling, which has made UK assets more than 10 per cent cheaper for those whose home currencies are dollar-linked.

That led to a brief spike in sales in the week after the vote, which agents say they are hoping will herald a new wave of interest among overseas buyers. But to revive a sinking market, those buyers drawn in by the prospect of bargains would need to outnumber those put off by the many uncertainties surrounding Brexit.